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Two Dimensional Kinematics

Today. Two Dimensional Kinematics. y. x. 2-Dimensions. X and Y are INDEPENDENT! (Just like Force) Break 2-D problem into two 1-D problems. 7. Kinematics in Two Dimensions. x = x 0 + v 0x t + 1/2 a x t 2 v x = v 0x + a x t v x 2 = v 0x 2 + 2a x  x.

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Two Dimensional Kinematics

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  1. Today Two Dimensional Kinematics

  2. y x 2-Dimensions • X and Y are INDEPENDENT! (Just like Force) • Break 2-D problem into two 1-D problems 7

  3. Kinematics in Two Dimensions • x = x0 + v0xt + 1/2 axt2 • vx = v0x +axt • vx2 = v0x2 + 2axx • y = y0 + v0yt + 1/2 ayt2 • vy = v0y +ayt • vy2 = v0y2 + 2ayy x andymotions areindependent! They share a common time t 21

  4. Projectile Motion Demo One marble is given an initial horizontal velocity, the other simply dropped. Which marble hits the ground first? A) dropped B) pushed C) They both hit the ground at the same time When ball hits depends on y only! y(t) = y0 + vyo + ½ ay t Same for both balls! 35

  5. Example: ball thrown from cliff • Use y components to find time vo= 20 m/s • Use x velocity and time to find horizontal distance 60m

  6. See text: 4-3 Shooting the Monkey... x= v0 t y= -1/2 g t2 x = x0 y= -1/2 g t2 40

  7. Dart hits the monkey! Shooting the Monkey... y= y0 - 1/2 g t2 • Still works even if you shoot upwards! y= v0yt - 1/2 g t2 41

  8. Vo=30m/s 200 Example: projectile • Find max height and distance Vo=30m/s Δy 200 Δx • Break Vo into x & y components

  9. Example: projectile Vo=30m/s Δy • 200 Δx

  10. Example: golf shot A golfer’s ball lands 30m behind a 20m tall tree. If he hits a ball at 50m/s at an angle of 40 degrees will the ball get over the tree? How do we solve this problem? • Find max height of ball and compare to height of tree • Find max distance of ball and compare to 30m • Find height of ball after traveling 30m in the horizontal 20m Vo=50m/s 400 30m

  11. Vo=50m/s 400 Example: golf shot • Will the ball get over the tree? 20m Vo=50m/s 400 30m

  12. Example: golf shot • Will the ball get over the tree? 20m Vo=50m/s 400 30m

  13. Summary of Concepts • X and Y directions are Independent! • Position, velocity and acceleration are vectors • “Share” t • F = m a applies in both x and y direction • Projective Motion • ax = 0 in horizontal direction • ay = g in vertical direction 50

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